Churn and Default

Introduction

Solar power is the fastest growing renewable energy source. Community solar projects lower the barrier to entry. This is accomplished by increasing the applicant pool by allowing those without rooftop access, such as renters or those in apartment buildings, and by lowering the financial burden of entry, as the fixed costs to install and operate the solar panels are collectivised rather than focused on one rooftop.

For potential customers, community solar contracts vary by their contract attributes. These include term length, cancellation fees, and potential savings rates relative to traditional utility bill companies. Given the importance of both the solar industry and the relatively incipient community solar industry, a dearth of research exists on how potential customer priorities are reflected in the likelihood of contract adoption.

This research seeks to fill this gap by developing quantitative measurements of community priorities in likelihood of contract adoption. An original data set comprised of potential community solar customers surveyed was collected. Along with respondents demographic information, draft contracts with varying degrees of contract attributes were shown to each participant and their contract adoption rates. Using a weighted logit model, the likelihood of contract adoption was analyzed by including predictors for various demographic data and contract attributes. Additionally, relative importance is through a multinomial logit model, allowing contract attributes and demographic information to be interpreted in predictive strength relative to respective reference groups.

Literature Review

to-do

Data

This research focuses on community shared solar (CSS) programs that are third-party owned and have participants subscribe to ongoing payments. Typically, within these programs, customers are given predefined, discrete contract terms rather than being able to compare multiple offerings or select their own terms. Our research is attempting to mimic this approach by giving customers a randomly assigned contract and surveying them on their willingness to adopt this program.

Descriptive Statistics

Summary Statistics
Variable	N	Percent	Variable	N	Percent
Sign Up	2986		Time Spent Reviewing Contracts	2986
… No	1215	40.7%	… 01 Less review	1202	40.3%
… Yes	1771	59.3%	… 02 More review	1784	59.7%
Contract Review Order	2985		Government Assistance	2986
… 01 First review	1492	50%	… 01 None, Unknown, or Other	1340	44.9%
… 02 Second review	1493	50%	… 02 At least one gov’t program	1646	55.1%
Savings Rate	2986		Race	2986
… 5% savings rate	1001	33.5%	… 01 White	1204	40.3%
… 10% savings rate	1003	33.6%	… 02 Black	580	19.4%
… 20% savings rate	982	32.9%	… 03 Hispanic	414	13.9%
Cancellation Fee	2986		… 04 Asian	434	14.5%
… 0	1495	50.1%	… 05 Other POC	354	11.9%
… 250	1491	49.9%	Homeownership	2986
Contract Length Pages	2986		… 01 Homeowner	1728	57.9%
… 10-page contract	1491	49.9%	… 02 Renter	1248	41.8%
… 20-page contract	1495	50.1%	… 03 Other	10	0.3%
Contract Length Years	2986		Income	2986
… 1-year contract	1496	50.1%	… 01 High	772	25.9%
… 25-year contract	1490	49.9%	… 02 Moderate income	1396	46.8%
Source	2986		… 03 Low income	818	27.4%
… 01 Qualtrics Panel	2520	84.4%	Familiar with CS	2986
… 02 Community	466	15.6%	… 01 Less familiar	1354	45.3%
			… 02 More familiar	1632	54.7%

Demographic Comparison

Descriptive Statistics, 8-State Region
Race	Census_Total	Survey_Total	Weight
White	52,150,851	602	86,629.32
Hispanic or Latino	24,830,970	207	119,956.38
Asian	9,585,168	217	44,171.28
Black or African American	9,540,566	290	32,898.50
Other - POC	3,841,546	177	21,703.65
Total	99,949,101	1,493	99,949,101.00

Descriptive Statistics, 8-State Region
Income	Census_Total	Survey_Total	Weight
1: Less than 30% AMI	10,158,670	218	46,599.40
2: Between 30-50% AMI	8,281,900	191	43,360.73
3: Between 50-80% AMI	10,865,560	360	30,182.11
4: Between 80-120% AMI	12,901,840	338	38,171.12
5: More than 120% AMI	29,350,940	386	76,038.71
Total	71,558,910	1,493	71,558,910.00

Descriptive Statistics, 8-State Region
x_hs	Census_Total	Survey_Total	Weight
01 Homeowner	21,679,273	864	25,091.75
02 Renter	14,590,602	624	23,382.38
Total	36,269,875	1,488	108,399,374.72

Sources:

Race: 2020 5-Year ACS, Table B03002 Homeownership: 2020 5 Year ACS, Table B25003 Income: CHAS

Crosstab Graphics

Savings Rate & Income

Savings Rate & Race

Race & Income

Cancellation Fee & Income

Cancellation Fee & Race

Contract Years & Income

Contract Years & Race

Methods

A number of independent variables will be used for both contract attributes and demographic data. Interaction variables will be tested for significant, along with a initial stepwise regression to determine which variables to initially include. The below equation is a summary of the full model used in this analysis. The dependent variable is a binary variable for contract adoption, $y_{signup}$, where 1 signifies the contract was adopted and 0 signifies it was not.

\[\begin{equation} y_{signup} = \beta_{0} + \beta_{1}x_{sr} +\beta_{2}x_{cly} +\beta_{3}x_{clp} +\beta_{4}x_{cf} + \\ \beta{5}x_{inc}+\beta_{6}x_{race} + \beta{7}x_{hs} +\beta_{8}x_{fam} + \beta_{9}x_{rev} + \beta_{10}x_{ord}+ e_{i} \end{equation}\]

where,

$x_{sr}$: savings rates on monthly energy bill in contracts, listed at either 5%, 10% or 20%
$x_{cly}$: contract length years, either 1 or 25 years
$x_{clp}$: contract length pages, either 10 or 20 pages
$x_{cf}$: cancellation fee, either zero or $250
$x_{inc}$: income, listed as Low (up to 50% of AMI), Moderate (50% - 120% of AMI), or High (>120% AMI)
$x_{race}$: Categories include Asian, Black or African American, Hispanic or Latino, White and Other POC
$x_{hs}$: Homeowner status for Homeowner, Renter or Other
$x_{fam}$: More or less familiar with community solar
$x_{rev}$: How much respondent reviewed the contract; up to half the contract review is captured by “less review”, over half and up to the whole contract is “more review”
$x_{ord}$: Contract review order, likely not necessary.

Other variables of interest to consider: government program - x_govt

Primary Analysis

to-do

add intro/dialogue

Regression Tables

Table 1

## 
## Regression Table 1
## ===========================================================================================
##                                                 Dependent variable:                        
##                          ------------------------------------------------------------------
##                                                       Sign Up                              
##                               (1)             (2)              (3)              (4)        
## -------------------------------------------------------------------------------------------
## Savings Rate 10%             0.125           0.126            0.126            0.127       
##                             (0.090)         (0.090)          (0.090)          (0.091)      
##                                                                                            
## Savings Rate 20%             0.089           0.090            0.090            0.082       
##                             (0.087)         (0.087)          (0.087)          (0.087)      
##                                                                                            
## Contract Length 25 Years                   -0.202***        -0.202***        -0.213***     
##                                             (0.076)          (0.076)          (0.076)      
##                                                                                            
## Contract Length 20 Pages                     -0.046          -0.046            -0.053      
##                                             (0.072)          (0.072)          (0.073)      
##                                                                                            
## Cancellation Fee 250                                          0.001            0.008       
##                                                              (0.075)          (0.075)      
##                                                                                            
## High Income                                                                    0.210       
##                                                                               (0.137)      
##                                                                                            
## Moderate Income                                                               0.561***     
##                                                                               (0.120)      
##                                                                                            
## Constant                    0.304***        0.426***        0.425***           0.118       
##                             (0.073)         (0.091)          (0.097)          (0.126)      
##                                                                                            
## -------------------------------------------------------------------------------------------
## Observations                 2,975           2,975            2,975            2,975       
## R2                           0.001           0.004            0.004            0.023       
## chi2                     1.964 (df = 2) 9.619** (df = 4) 9.619* (df = 5) 51.020*** (df = 7)
## ===========================================================================================
## Note:                                                           *p<0.1; **p<0.05; ***p<0.01

Table 2

## 
## Regression Table 2
## ==========================================================================================================
##                                                         Dependent variable:                               
##                          ---------------------------------------------------------------------------------
##                                                               Sign Up                                     
##                                  (1)                 (2)                 (3)                  (4)         
## ----------------------------------------------------------------------------------------------------------
## Savings Rate 10%                0.115               0.120               0.158*               0.159*       
##                                (0.091)             (0.091)             (0.096)              (0.096)       
##                                                                                                           
## Savings Rate 20%                0.077               0.078               0.117                0.120        
##                                (0.088)             (0.088)             (0.094)              (0.094)       
##                                                                                                           
## Contract Length 25 Years      -0.209***           -0.223***           -0.229***            -0.226***      
##                                (0.076)             (0.077)             (0.081)              (0.081)       
##                                                                                                           
## Contract Length 20 Pages       -0.065              -0.065               -0.067               -0.057       
##                                (0.073)             (0.073)             (0.076)              (0.076)       
##                                                                                                           
## Cancellation Fee 250            0.013               0.012               0.037                0.041        
##                                (0.075)             (0.076)             (0.081)              (0.081)       
##                                                                                                           
## High Income                    0.290**              0.231              0.356**              0.348**       
##                                (0.144)             (0.146)             (0.157)              (0.158)       
##                                                                                                           
## Moderate Income               0.601***            0.540***             0.535***             0.526***      
##                                (0.122)             (0.124)             (0.132)              (0.132)       
##                                                                                                           
## Black                           0.075               0.162               0.089                0.073        
##                                (0.146)             (0.148)             (0.156)              (0.157)       
##                                                                                                           
## Hispanic                        0.224              0.319**              0.169                0.160        
##                                (0.153)             (0.158)             (0.169)              (0.170)       
##                                                                                                           
## Asian                          -0.136              -0.072               -0.017               0.004        
##                                (0.151)             (0.154)             (0.164)              (0.164)       
##                                                                                                           
## Other                          0.303*              0.376**             0.440**              0.442**       
##                                (0.177)             (0.179)             (0.189)              (0.190)       
##                                                                                                           
## Renter                                            -0.327***             -0.092               -0.070       
##                                                    (0.108)             (0.116)              (0.116)       
##                                                                                                           
## More Familiar                                                          1.470***             1.478***      
##                                                                        (0.110)              (0.110)       
##                                                                                                           
## More Reviewed                                                                               0.256**       
##                                                                                             (0.101)       
##                                                                                                           
## Constant                        0.026               0.167             -0.738***            -0.905***      
##                                (0.149)             (0.157)             (0.179)              (0.189)       
##                                                                                                           
## ----------------------------------------------------------------------------------------------------------
## Observations                    2,975               2,975               2,975                2,975        
## R2                              0.028               0.035               0.178                0.182        
## chi2                     62.852*** (df = 11) 79.180*** (df = 12) 421.368*** (df = 13) 430.983*** (df = 14)
## ==========================================================================================================
## Note:                                                                          *p<0.1; **p<0.05; ***p<0.01

Odds Ratios

Table 1

## 
## Odds Ratio, Table 1
## ===========================================================================================
##                                                 Dependent variable:                        
##                          ------------------------------------------------------------------
##                                                       Sign Up                              
##                               (1)             (2)              (3)              (4)        
## -------------------------------------------------------------------------------------------
## Savings Rate 10%             1.133           1.134            1.134            1.136       
##                             (1.094)         (1.094)          (1.094)          (1.095)      
##                                                                                            
## Savings Rate 20%             1.093           1.095            1.095            1.085       
##                             (1.091)         (1.091)          (1.091)          (1.091)      
##                                                                                            
## Contract Length 25 Years                     0.817            0.817            0.808       
##                                             (1.079)          (1.079)          (1.079)      
##                                                                                            
## Contract Length 20 Pages                     0.955            0.955            0.949       
##                                             (1.075)          (1.075)          (1.076)      
##                                                                                            
## Cancellation Fee 250                                          1.001            1.008       
##                                                              (1.078)          (1.078)      
##                                                                                            
## High Income                                                                    1.234       
##                                                                               (1.147)      
##                                                                                            
## Moderate Income                                                                1.752       
##                                                                               (1.127)      
##                                                                                            
## Constant                     1.355           1.531            1.530            1.126       
##                             (1.076)         (1.096)          (1.101)          (1.134)      
##                                                                                            
## -------------------------------------------------------------------------------------------
## Observations                 2,975           2,975            2,975            2,975       
## R2                           0.001           0.004            0.004            0.023       
## chi2                     1.964 (df = 2) 9.619** (df = 4) 9.619* (df = 5) 51.020*** (df = 7)
## ===========================================================================================
## Note:                                                           *p<0.1; **p<0.05; ***p<0.01

Table 2

## 
## Odds Ratio, Table 2
## ==========================================================================================================
##                                                         Dependent variable:                               
##                          ---------------------------------------------------------------------------------
##                                                               Sign Up                                     
##                                  (1)                 (2)                 (3)                  (4)         
## ----------------------------------------------------------------------------------------------------------
## Savings Rate 10%                1.121               1.128               1.172                1.172        
##                                (1.095)             (1.096)             (1.101)              (1.101)       
##                                                                                                           
## Savings Rate 20%                1.080               1.081               1.124                1.127        
##                                (1.092)             (1.092)             (1.098)              (1.098)       
##                                                                                                           
## Contract Length 25 Years        0.812               0.800               0.795                0.798        
##                                (1.079)             (1.080)             (1.085)              (1.085)       
##                                                                                                           
## Contract Length 20 Pages        0.937               0.937               0.935                0.944        
##                                (1.076)             (1.076)             (1.079)              (1.079)       
##                                                                                                           
## Cancellation Fee 250            1.014               1.012               1.038                1.042        
##                                (1.078)             (1.078)             (1.084)              (1.084)       
##                                                                                                           
## High Income                     1.336               1.260               1.427                1.416        
##                                (1.155)             (1.157)             (1.170)              (1.171)       
##                                                                                                           
## Moderate Income                 1.825               1.716               1.708                1.692        
##                                (1.129)             (1.132)             (1.141)              (1.141)       
##                                                                                                           
## Black                           1.078               1.176               1.094                1.076        
##                                (1.157)             (1.159)             (1.169)              (1.170)       
##                                                                                                           
## Hispanic                        1.251               1.376               1.184                1.173        
##                                (1.166)             (1.171)             (1.184)              (1.185)       
##                                                                                                           
## Asian                           0.873               0.931               0.983                1.004        
##                                (1.163)             (1.166)             (1.179)              (1.179)       
##                                                                                                           
## Other                           1.354               1.456               1.553                1.556        
##                                (1.193)             (1.196)             (1.209)              (1.209)       
##                                                                                                           
## Renter                                              0.721               0.912                0.932        
##                                                    (1.114)             (1.123)              (1.123)       
##                                                                                                           
## More Familiar                                                          4.349***             4.382***      
##                                                                        (1.116)              (1.116)       
##                                                                                                           
## More Reviewed                                                                                1.292        
##                                                                                             (1.106)       
##                                                                                                           
## Constant                        1.026               1.182               0.478                0.404        
##                                (1.160)             (1.170)             (1.196)              (1.208)       
##                                                                                                           
## ----------------------------------------------------------------------------------------------------------
## Observations                    2,975               2,975               2,975                2,975        
## R2                              0.028               0.035               0.178                0.182        
## chi2                     62.852*** (df = 11) 79.180*** (df = 12) 421.368*** (df = 13) 430.983*** (df = 14)
## ==========================================================================================================
## Note:                                                                          *p<0.1; **p<0.05; ***p<0.01

Discussion

Main Takeaways

Table 1

Contract length of 25 years compared to 1 year remained a significant deterrent to contract acceptance rates.
Relative to low income, moderate and higher income respondents were more likely to accept the contract, holding th effect of savings rate, cancellation fee, and contract length constant.

Table 2

Contract lenght remained a constant deterrance
Homeowner status, rent vs homeowner, was not observed as a statistically significant effect on signup rate. Likely some multicollinearity due to effect (sign) varying from model 2 to model 4.
After including familiarity and reviewed dummies, savings rate becomes statistically significant effect on likelihood of contract adoption.
More familiar with community solar implies significantly more likely to adopt contract (suggests importance of education) - odds ratio of >4 in model 3 and 4
In looking at contract adoption by race, Hispanics were the only group observed with a statistically significant effect in models 1 and 2. Relative to white, hispanic rates were higher. This effect is negated after additional IVs are introduces in models 3 and 4.

From Table 1, four models are presented analyzing changes in probability of sign up. Controlling for all other variables, contract length and income were found to have statistically significant effects on the rate of sign up. Contract length was found to have a strong negative impact on probability of contract adoption. For example, holding all variables constant, from model 2 we see that the odds ratio for contract length of 25 years is 0.782, meaning the group with contracts of 25 years are 0.782 times as likely as the group with contracts of 1 year of signing up, or a 21.8% decrease in odds of signing up.

Interestingly, lower income respondents were much less likely to adopt the contract, even when controlling for savings rate, contract length and number of pages, and cancellation fees. High income and medium income respondents were 1.3 and 1.7 times the odds to adopt the contract compared to low income respondents, controlling for contract attributes.

Secondary Analysis

The secondary analysis will include an ordered logit model to investigate the degree of which the same independent variables above influence the likert scale questions asked in the survey. Ordered logit models are commonly utilized with outputs of interest are categorized in discrete sequences, such as a Likert scale.

Churn and Default